The Trim tool is used to re-limit curves to other objects. Located in the Curve Utilities palette this tool is one of the most frequently used tools to modify curve extents.
Several useful tips related to the Trim tool are:
Another useful tip when using the Trim tool is using it in conjunction with Select All. Selected objects not only serve as a trim boundary, but can be trimmed as well depending on where you click with the mouse. Check out the video below demonstrating the Trim tool.